STATS522_HW2.ipynb

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  "metadata": {
    "colab": {
      "name": "STATS522-HW2.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMaPritJBDWqYdryDM7PAld",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jctan05/biostats_HW/blob/master/STATS522_HW2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IKhRT4DS1clU",
        "colab_type": "text"
      },
      "source": [
        "# STATS522 - John Tan"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s5TEoBCNm_46",
        "colab_type": "text"
      },
      "source": [
        "1. Use the data file fev.txt posted on Canvas for this problem. A researcher measured forced expiratory volume, which is a measure of lung capacity, among 300 healthy children. Variables included in the data are: Age (in years), FEV (in liters), and Height (in inches). We would like to conduct simple regression analysis between FEV (as the outcome) and age (as the predictor).\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "Create a scatter plot of FEV against age. What do you observe? Comment on your findings.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d66OuTDjmDrj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "from scipy import stats\n",
        "import statsmodels.api as sm\n",
        "\n",
        "sns.set('notebook')\n",
        "\n",
        "from statsmodels.stats.diagnostic import het_white, het_arch, het_breuschpagan"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bp0hGclUmLKl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df = pd.read_csv('fev.txt', names=['Age', 'FEV', 'Height'], delim_whitespace=True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Au0rm6eDmOze",
        "colab_type": "code",
        "outputId": "4b34fe9f-054f-4ff0-e49c-d701b20ee96f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        }
      },
      "source": [
        "df.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
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              "    }\n",
              "\n",
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              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Age</th>\n",
              "      <th>FEV</th>\n",
              "      <th>Height</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>9</td>\n",
              "      <td>1.708</td>\n",
              "      <td>57.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>8</td>\n",
              "      <td>1.724</td>\n",
              "      <td>67.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>7</td>\n",
              "      <td>1.720</td>\n",
              "      <td>54.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>9</td>\n",
              "      <td>1.558</td>\n",
              "      <td>53.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>9</td>\n",
              "      <td>1.895</td>\n",
              "      <td>57.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Age    FEV  Height\n",
              "0    9  1.708    57.0\n",
              "1    8  1.724    67.5\n",
              "2    7  1.720    54.5\n",
              "3    9  1.558    53.0\n",
              "4    9  1.895    57.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zR92KO1ymgCo",
        "colab_type": "code",
        "outputId": "f58142ec-6fcf-46c5-efec-6b3a45f39a1d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 305
        }
      },
      "source": [
        "sns.scatterplot(x=\"Age\", y=\"FEV\", data=df)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7effbe3b3518>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
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JnMUwBL4pPYNl/+/j4AXpqYeGoHe3q6BKll9QcroGc3J2h31/ffZIpHZuH4UWtUx5ZS0W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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "soHNEcThnYh0",
        "colab_type": "text"
      },
      "source": [
        "It seems that there is a weak positive correlation of Age vs. FEV. However the variable Age may add error to the model due to its categorical nature.\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "Run a simple linear regression model using FEV as the outcome and age as the 2\n",
        "predictor variable. Report the estimated regression equation and $R^{2}$. Is there a significant association between FEV and age?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jw0z74E4nSju",
        "colab_type": "code",
        "outputId": "6267e0e6-61d0-4be7-9ebd-d1ca27aa1f5e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        }
      },
      "source": [
        "Y = df['FEV']\n",
        "X = df['Age']\n",
        "X = sm.add_constant(X) # add constant because statsmodel doesn't have it by default\n",
        "\n",
        "model = sm.OLS(Y, X).fit()\n",
        "\n",
        "model.summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/numpy/core/fromnumeric.py:2495: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
            "  return ptp(axis=axis, out=out, **kwargs)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>           <td>FEV</td>       <th>  R-squared:         </th> <td>   0.430</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.429</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   225.3</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Tue, 21 Jan 2020</td> <th>  Prob (F-statistic):</th> <td>2.60e-38</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>01:14:26</td>     <th>  Log-Likelihood:    </th> <td> -141.77</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>   300</td>      <th>  AIC:               </th> <td>   287.5</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>   298</td>      <th>  BIC:               </th> <td>   294.9</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th> <td>    0.3096</td> <td>    0.117</td> <td>    2.646</td> <td> 0.009</td> <td>    0.079</td> <td>    0.540</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Age</th>   <td>    0.2305</td> <td>    0.015</td> <td>   15.008</td> <td> 0.000</td> <td>    0.200</td> <td>    0.261</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td> 8.547</td> <th>  Durbin-Watson:     </th> <td>   1.548</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.014</td> <th>  Jarque-Bera (JB):  </th> <td>   8.473</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td> 0.373</td> <th>  Prob(JB):          </th> <td>  0.0145</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 3.347</td> <th>  Cond. No.          </th> <td>    40.3</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:                    FEV   R-squared:                       0.430\n",
              "Model:                            OLS   Adj. R-squared:                  0.429\n",
              "Method:                 Least Squares   F-statistic:                     225.3\n",
              "Date:                Tue, 21 Jan 2020   Prob (F-statistic):           2.60e-38\n",
              "Time:                        01:14:26   Log-Likelihood:                -141.77\n",
              "No. Observations:                 300   AIC:                             287.5\n",
              "Df Residuals:                     298   BIC:                             294.9\n",
              "Df Model:                           1                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const          0.3096      0.117      2.646      0.009       0.079       0.540\n",
              "Age            0.2305      0.015     15.008      0.000       0.200       0.261\n",
              "==============================================================================\n",
              "Omnibus:                        8.547   Durbin-Watson:                   1.548\n",
              "Prob(Omnibus):                  0.014   Jarque-Bera (JB):                8.473\n",
              "Skew:                           0.373   Prob(JB):                       0.0145\n",
              "Kurtosis:                       3.347   Cond. No.                         40.3\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0Kzm1N-oqDeg",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "The estimated regression line is $FEV = 0.3096 + 0.2305 * Age$\n",
        "\n",
        "The $R^{2}$ is 0.430. Yes, there is a significant association between FEV and age.\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "c. Produce a residual plot against predicted values, as well as a normal probability plot of residuals. Are regression assumptions met? Comment on your findings."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Sn3-pgQiot0q",
        "colab_type": "code",
        "outputId": "4e5b6960-64b4-4fc8-953d-00db91422f61",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "source": [
        "sns.residplot(x=\"Age\", y=\"FEV\", data=df)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7effbb63e5c0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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eXl624d97gzf0C1MUhuLibDidNkgSi3pvwoDvvZuvugAHGtpx+AMFpzq96M/w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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "riDhN2ENrXAs",
        "colab_type": "code",
        "outputId": "a1471532-36a4-448b-f43e-1c8fc6116ea7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        }
      },
      "source": [
        "trash_tuple = stats.probplot(x=sm.OLS(Y, X).fit().resid, plot=sns.mpl.pyplot, fit=True)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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XnxrfJwPoor5YFCTz5s1jxowZREdHExoaSkpKCrt27eKFF15o6PqEELVYsCIO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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H7uUbWqknW0Q",
        "colab_type": "text"
      },
      "source": [
        "No, it does not meet regression assumptions because the residual plot shows that error variance increases by age.\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "Conduct White’s test for homoscedasticity. What do you find? Interpret the result."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2UDcOHcKroVy",
        "colab_type": "code",
        "outputId": "c4a4dd8f-9b15-4e45-e511-fe87af494781",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "white_test = het_white(model.resid, X)\n",
        "\n",
        "labels = ['LM Statistic', 'LM-Test p-value', 'F-Statistic', 'F-Test p-value']\n",
        "\n",
        "print(dict(zip(labels, white_test)))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'LM Statistic': 20.91357222405319, 'LM-Test p-value': 2.8752492120466965e-05, 'F-Statistic': 11.127970285123121, 'F-Test p-value': 2.1862163073088987e-05}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zbFfAjYrt3MU",
        "colab_type": "text"
      },
      "source": [
        "Because White's test is significant, we conclude that the model is heteroscedastic.\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "Run the Box-Cox procedure and find an appropriate power transformation Y λ . What is the “best” value of λ that minimizes MSE according to the output? What is the “convenient” value of λ recommended by the procedure? What is the transformation suggested by this “convenient” λ ?\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fBAGyJOstvnj",
        "colab_type": "code",
        "outputId": "d54722ad-6cf1-469a-fd7c-c2d43af8fa2f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "Y_xformed, lambda_val = stats.boxcox(Y)\n",
        "print(lambda_val)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.40781411347525753\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pSXSa1iDtwfv",
        "colab_type": "text"
      },
      "source": [
        "The \"best\" value of $\\lambda$ that minimizes MSE is 0.4078. The \"convenient\" value would be 0.5. This suggests that the transformation should be as square root transformation."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y7rON3m1sGHk",
        "colab_type": "code",
        "outputId": "3e69f8ac-04c5-477c-a928-df2db2e1a90b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        }
      },
      "source": [
        "model = sm.OLS(Y_xformed, X).fit()\n",
        "\n",
        "model.summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.456</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.455</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   250.2</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Tue, 21 Jan 2020</td> <th>  Prob (F-statistic):</th> <td>2.46e-41</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>01:14:26</td>     <th>  Log-Likelihood:    </th> <td> -9.1743</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>   300</td>      <th>  AIC:               </th> <td>   22.35</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>   298</td>      <th>  BIC:               </th> <td>   29.76</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th> <td>   -0.3700</td> <td>    0.075</td> <td>   -4.919</td> <td> 0.000</td> <td>   -0.518</td> <td>   -0.222</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Age</th>   <td>    0.1562</td> <td>    0.010</td> <td>   15.817</td> <td> 0.000</td> <td>    0.137</td> <td>    0.176</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td> 0.306</td> <th>  Durbin-Watson:     </th> <td>   1.535</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.858</td> <th>  Jarque-Bera (JB):  </th> <td>   0.444</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td>-0.004</td> <th>  Prob(JB):          </th> <td>   0.801</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 2.812</td> <th>  Cond. No.          </th> <td>    40.3</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:                      y   R-squared:                       0.456\n",
              "Model:                            OLS   Adj. R-squared:                  0.455\n",
              "Method:                 Least Squares   F-statistic:                     250.2\n",
              "Date:                Tue, 21 Jan 2020   Prob (F-statistic):           2.46e-41\n",
              "Time:                        01:14:26   Log-Likelihood:                -9.1743\n",
              "No. Observations:                 300   AIC:                             22.35\n",
              "Df Residuals:                     298   BIC:                             29.76\n",
              "Df Model:                           1                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const         -0.3700      0.075     -4.919      0.000      -0.518      -0.222\n",
              "Age            0.1562      0.010     15.817      0.000       0.137       0.176\n",
              "==============================================================================\n",
              "Omnibus:                        0.306   Durbin-Watson:                   1.535\n",
              "Prob(Omnibus):                  0.858   Jarque-Bera (JB):                0.444\n",
              "Skew:                          -0.004   Prob(JB):                        0.801\n",
              "Kurtosis:                       2.812   Cond. No.                         40.3\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y4ZeluQF24t_",
        "colab_type": "code",
        "outputId": "d2908170-bb83-4883-e81a-8d4ab97cda4c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "source": [
        "sns.scatterplot(df['Age'], Y_xformed)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7effba2e9f98>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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njoaHO4vT9VDXLN0b8VJcrDxPuwBgSjfJdNHt9U1gSm9okaL0S8tgAmDlL/4n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\nIjIUAzwRkaEY4ImIDPX/AeCm8cXGnhdzAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qqJSNEFa4fFD",
        "colab_type": "text"
      },
      "source": [
        "The regression equation is $FVE = -0.37 + 0.1562 * Age$ The $R^2$ improved from 0.430 to 0.456. However I expected there to be more improvement than that.\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "g. Repeat parts c) and d) above, using the transformed Y. Did the transformation help?\n",
        "Comment on your findings.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ynw4cqhP3Kom",
        "colab_type": "code",
        "outputId": "5b62ace0-22ea-4262-a22c-bf46f77a86e9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "source": [
        "sns.residplot(x=df[\"Age\"], y=Y_xformed)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7effba25c390>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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fK0hLs57y/fDj/tdW/++6//jk116KmSE4xBwkWZLCXnsnv7YS8rVnkgcNnEoA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\nQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P22jTX9u6ha3",
        "colab_type": "code",
        "outputId": "9247ddda-8234-4bab-dd58-2b43aa58d3c7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        }
      },
      "source": [
        "trash_tuple = stats.probplot(x=sm.OLS(Y_xformed, X).fit().resid, plot=sns.mpl.pyplot, fit=True)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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v5WfPLkR7dkanVFU4h41KwbPD5SpE3F61QXL58mXat29Pq1Z/jVT19vbm3Xff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\nQSJJimKQSJKivAO7YUuB0pe3NwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fZECKo2Z68jt",
        "colab_type": "code",
        "outputId": "5063e5c6-53f5-4296-8ccf-7199cf51be7b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "white_test = het_white(model.resid, X)\n",
        "\n",
        "labels = ['LM Statistic', 'LM-Test p-value', 'F-Statistic', 'F-Test p-value']\n",
        "\n",
        "print(dict(zip(labels, white_test)))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'LM Statistic': 8.394752427469498, 'LM-Test p-value': 0.015034973670834726, 'F-Statistic': 4.275028470360953, 'F-Test p-value': 0.0147774986648223}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PGVKRZo99M7I",
        "colab_type": "text"
      },
      "source": [
        "The transformation helped a little bit but it is still not homoscedastic. \n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "Refer to the SENIC data set in the previous assignment. Two models have been proposed for predicting the average length of stay in a hospital (Y: LOS). Model 1 utilizes as predictor variables age (X1), infection risk (X2), and available facilities and services (X3). Model 2 uses as predictor variables number of beds (X1), infection risk (X2), and available facilities and services (X3).\n",
        "*** Make sure to exclude IDs 47 and 112 prior to analysis below. There should be n = 111 after exclusion. Check # of obs ***"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BRcGQaFP7OCO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = pd.read_csv('SENIC.txt', header= None, names=[\"id\", \"los\", \"age\", \"infect\", \"culture\", \"xray\", \"beds\",  \n",
        "                  \"school\", \"region\", \"census\", \"nurses\", \"service\"], delim_whitespace=True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YUi_Oy2I9a4w",
        "colab_type": "code",
        "outputId": "a7f8f9a2-d170-452f-99ef-b77d3d4a7af6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "print('Before clean {}'.format(len(data)))\n",
        "data = data[data['id'] != 47]\n",
        "data = data[data['id'] != 112]\n",
        "print('After clean {}'.format(len(data)))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Before clean 113\n",
            "After clean 111\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DsyDqUcL-NVG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = data[['id', 'los', 'age', 'beds', 'infect', 'service']]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e1mF6EHv_ZJT",
        "colab_type": "text"
      },
      "source": [
        "Produce a scatterplot matrix and a correlation matrix among the outcome and all predictor variables involved in the two models. What do you observe? Which predictor variable has the highest correlation with the average length of stay? Comment on your findings."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bw6qIIzl_LOz",
        "colab_type": "code",
        "outputId": "bf3547cd-d1a7-42ab-92ec-8701c798c2ad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "sns.pairplot(data)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<seaborn.axisgrid.PairGrid at 0x7effba1c3780>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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MS3oQRkgfCaLOsTLMF68MaFnc3YdOY+2dM/Gx9iSYzWApK8dHkApzJbysbrA7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\nDeuKMXZOkCM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dpOPpl0riNZTHTxB0Y0sQBLQnzHOtE3rxrXXitbWOsPQeRsc5rLm/Enrx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iVn+CzMsJW6pl5WQdx8z3L2Xe5ZVmZsc9NIxBtx83XT81ailyxow7bdBzD3ynP1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\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KengBxsEl8Bg3ol9YuxfmCGGiXb1+M4tdp+QXLdlWL6fFayLI47i9MwBwXFzjWJ0LBI7H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\nhBMAAAAAAMBVhBMAAAAAAMBVvwGqDujtxe1z+QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1080x1080 with 42 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U1xNbKWs_Ufa",
        "colab_type": "code",
        "outputId": "47435044-928c-4a59-c8aa-d63e0ff84de2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 237
        }
      },
      "source": [
        "data.corr()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>id</th>\n",
              "      <th>los</th>\n",
              "      <th>age</th>\n",
              "      <th>beds</th>\n",
              "      <th>infect</th>\n",
              "      <th>service</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>id</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.098503</td>\n",
              "      <td>0.031926</td>\n",
              "      <td>-0.085250</td>\n",
              "      <td>-0.231652</td>\n",
              "      <td>-0.118665</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>los</th>\n",
              "      <td>-0.098503</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.122205</td>\n",
              "      <td>0.378011</td>\n",
              "      <td>0.549467</td>\n",
              "      <td>0.367860</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>age</th>\n",
              "      <td>0.031926</td>\n",
              "      <td>0.122205</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.085716</td>\n",
              "      <td>-0.028424</td>\n",
              "      <td>-0.056921</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beds</th>\n",
              "      <td>-0.085250</td>\n",
              "      <td>0.378011</td>\n",
              "      <td>-0.085716</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.344461</td>\n",
              "      <td>0.798442</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>infect</th>\n",
              "      <td>-0.231652</td>\n",
              "      <td>0.549467</td>\n",
              "      <td>-0.028424</td>\n",
              "      <td>0.344461</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.401806</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>service</th>\n",
              "      <td>-0.118665</td>\n",
              "      <td>0.367860</td>\n",
              "      <td>-0.056921</td>\n",
              "      <td>0.798442</td>\n",
              "      <td>0.401806</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "               id       los       age      beds    infect   service\n",
              "id       1.000000 -0.098503  0.031926 -0.085250 -0.231652 -0.118665\n",
              "los     -0.098503  1.000000  0.122205  0.378011  0.549467  0.367860\n",
              "age      0.031926  0.122205  1.000000 -0.085716 -0.028424 -0.056921\n",
              "beds    -0.085250  0.378011 -0.085716  1.000000  0.344461  0.798442\n",
              "infect  -0.231652  0.549467 -0.028424  0.344461  1.000000  0.401806\n",
              "service -0.118665  0.367860 -0.056921  0.798442  0.401806  1.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BEAkpqTt_zEV",
        "colab_type": "text"
      },
      "source": [
        "It seems like `los` is not a normal distribution. `infect` has the highest correlation with the average length of stay. To me, that makes sense because getting an infection is very common in hospitals.\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "b. For each of the two proposed models, fit the regression model with three predictor variables. Report the estimated regression equations. Give your interpretation on βˆ\n",
        "(only for the regression coefficient of X1) for each of the equations."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cLpRczBG_ecq",
        "colab_type": "code",
        "outputId": "7e48020c-6856-44bf-f1f5-6f205031406d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 549
        }
      },
      "source": [
        "# Mode1 1: age, infect, service\n",
        "\n",
        "X1 = data[['age', 'infect', 'service']]\n",
        "X1 = sm.add_constant(X1) # add constant because statsmodel doesn't have it by default\n",
        "y1 = data['los']\n",
        "\n",
        "model1 = sm.OLS(y1, X1).fit()\n",
        "\n",
        "model1.summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/numpy/core/fromnumeric.py:2495: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
            "  return ptp(axis=axis, out=out, **kwargs)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>           <td>los</td>       <th>  R-squared:         </th> <td>   0.349</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.331</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   19.12</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Tue, 21 Jan 2020</td> <th>  Prob (F-statistic):</th> <td>5.29e-10</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>01:14:38</td>     <th>  Log-Likelihood:    </th> <td> -176.29</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>   111</td>      <th>  AIC:               </th> <td>   360.6</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>   107</td>      <th>  BIC:               </th> <td>   371.4</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "     <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>   <td>    3.8412</td> <td>    1.463</td> <td>    2.625</td> <td> 0.010</td> <td>    0.941</td> <td>    6.742</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>age</th>     <td>    0.0485</td> <td>    0.026</td> <td>    1.872</td> <td> 0.064</td> <td>   -0.003</td> <td>    0.100</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>infect</th>  <td>    0.5326</td> <td>    0.095</td> <td>    5.635</td> <td> 0.000</td> <td>    0.345</td> <td>    0.720</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>service</th> <td>    0.0178</td> <td>    0.008</td> <td>    2.150</td> <td> 0.034</td> <td>    0.001</td> <td>    0.034</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td> 0.148</td> <th>  Durbin-Watson:     </th> <td>   2.143</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.929</td> <th>  Jarque-Bera (JB):  </th> <td>   0.263</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td> 0.079</td> <th>  Prob(JB):          </th> <td>   0.877</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 2.821</td> <th>  Cond. No.          </th> <td>    884.</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:                    los   R-squared:                       0.349\n",
              "Model:                            OLS   Adj. R-squared:                  0.331\n",
              "Method:                 Least Squares   F-statistic:                     19.12\n",
              "Date:                Tue, 21 Jan 2020   Prob (F-statistic):           5.29e-10\n",
              "Time:                        01:14:38   Log-Likelihood:                -176.29\n",
              "No. Observations:                 111   AIC:                             360.6\n",
              "Df Residuals:                     107   BIC:                             371.4\n",
              "Df Model:                           3                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const          3.8412      1.463      2.625      0.010       0.941       6.742\n",
              "age            0.0485      0.026      1.872      0.064      -0.003       0.100\n",
              "infect         0.5326      0.095      5.635      0.000       0.345       0.720\n",
              "service        0.0178      0.008      2.150      0.034       0.001       0.034\n",
              "==============================================================================\n",
              "Omnibus:                        0.148   Durbin-Watson:                   2.143\n",
              "Prob(Omnibus):                  0.929   Jarque-Bera (JB):                0.263\n",
              "Skew:                           0.079   Prob(JB):                        0.877\n",
              "Kurtosis:                       2.821   Cond. No.                         884.\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MFGNRIjjBLKT",
        "colab_type": "code",
        "outputId": "f396e25d-0835-43e0-ced6-581e4264f7b4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 584
        }
      },
      "source": [
        "# Mode1 2: beds, infect, service\n",
        "\n",
        "X2 = data[['beds', 'infect', 'service']]\n",
        "X2 = sm.add_constant(X2) # add constant because statsmodel doesn't have it by default\n",
        "y2 = data['los']\n",
        "\n",
        "model2 = sm.OLS(y2, X2).fit()\n",
        "\n",
        "model2.summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/numpy/core/fromnumeric.py:2495: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
            "  return ptp(axis=axis, out=out, **kwargs)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>           <td>los</td>       <th>  R-squared:         </th> <td>   0.342</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.324</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   18.57</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Tue, 21 Jan 2020</td> <th>  Prob (F-statistic):</th> <td>9.00e-10</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>01:14:38</td>     <th>  Log-Likelihood:    </th> <td> -176.86</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>   111</td>      <th>  AIC:               </th> <td>   361.7</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>   107</td>      <th>  BIC:               </th> <td>   372.5</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "     <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>   <td>    6.7518</td> <td>    0.477</td> <td>   14.156</td> <td> 0.000</td> <td>    5.806</td> <td>    7.697</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>beds</th>    <td>    0.0016</td> <td>    0.001</td> <td>    1.547</td> <td> 0.125</td> <td>   -0.000</td> <td>    0.004</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>infect</th>  <td>    0.5252</td> <td>    0.095</td> <td>    5.524</td> <td> 0.000</td> <td>    0.337</td> <td>    0.714</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>service</th> <td>    0.0016</td> <td>    0.013</td> <td>    0.125</td> <td> 0.901</td> <td>   -0.024</td> <td>    0.027</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td> 1.076</td> <th>  Durbin-Watson:     </th> <td>   2.087</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.584</td> <th>  Jarque-Bera (JB):  </th> <td>   1.119</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td> 0.227</td> <th>  Prob(JB):          </th> <td>   0.571</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 2.812</td> <th>  Cond. No.          </th> <td>1.30e+03</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.3e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:                    los   R-squared:                       0.342\n",
              "Model:                            OLS   Adj. R-squared:                  0.324\n",
              "Method:                 Least Squares   F-statistic:                     18.57\n",
              "Date:                Tue, 21 Jan 2020   Prob (F-statistic):           9.00e-10\n",
              "Time:                        01:14:38   Log-Likelihood:                -176.86\n",
              "No. Observations:                 111   AIC:                             361.7\n",
              "Df Residuals:                     107   BIC:                             372.5\n",
              "Df Model:                           3                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const          6.7518      0.477     14.156      0.000       5.806       7.697\n",
              "beds           0.0016      0.001      1.547      0.125      -0.000       0.004\n",
              "infect         0.5252      0.095      5.524      0.000       0.337       0.714\n",
              "service        0.0016      0.013      0.125      0.901      -0.024       0.027\n",
              "==============================================================================\n",
              "Omnibus:                        1.076   Durbin-Watson:                   2.087\n",
              "Prob(Omnibus):                  0.584   Jarque-Bera (JB):                1.119\n",
              "Skew:                           0.227   Prob(JB):                        0.571\n",
              "Kurtosis:                       2.812   Cond. No.                     1.30e+03\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The condition number is large, 1.3e+03. This might indicate that there are\n",
              "strong multicollinearity or other numerical problems.\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_9DUj9yHBk1R",
        "colab_type": "text"
      },
      "source": [
        "Model 1:\n",
        "\n",
        "$los = 1.3865 + 0.0837 * age + 0.6584 * infect + 0.0217 * service$\n",
        "\n",
        "Model 2:\n",
        "\n",
        "$los = 6.4674 + 0.0030 * beds + 0.6477 * infect - 0.0093 * service$\n",
        "\n",
        "Because age is a bigger coefficient than beds, it is also a greater predictor. Thus Model 1 is more accurate.\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "Report MSE and R-square for each model. Using R2 as the criterion, is one model clearly\n",
        "preferable in terms of this measure?\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fBryf0PeBig3",
        "colab_type": "code",
        "outputId": "2d6a0107-b234-4f0b-d3d0-f8cb9f00a596",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        }
      },
      "source": [
        "# MSE: https://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.OLSResults.html\n",
        "# 'mse_resid',  the residual sum of squares divided by the number of degrees of freedom\n",
        "# 'rsquared',\n",
        "def mse_and_r_squared(model):\n",
        "    mse = model.mse_resid\n",
        "    r2 = model.rsquared\n",
        "    return mse, r2\n",
        "\n",
        "m1, r1 = mse_and_r_squared(model1)\n",
        "m2, r2 = mse_and_r_squared(model2)\n",
        "\n",
        "mlst = [m1, m2]\n",
        "rlst = [r1, r2]\n",
        "\n",
        "R2_df = pd.DataFrame(list(zip(mlst, rlst)), index =['Model 1', 'Model 2'], columns = ['MSE', 'R2'])\n",
        "\n",
        "R2_df.T"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Model 1</th>\n",
              "      <th>Model 2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>MSE</th>\n",
              "      <td>1.455422</td>\n",
              "      <td>1.470205</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R2</th>\n",
              "      <td>0.349041</td>\n",
              "      <td>0.342429</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      Model 1   Model 2\n",
              "MSE  1.455422  1.470205\n",
              "R2   0.349041  0.342429"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pbZ1VUIYDZwH",
        "colab_type": "text"
      },
      "source": [
        "No, which model is better is unclear from the R-squared.\n",
        "\n",
        "---\n",
        "\n",
        "For Model 1, produce a data set containing predicted values and residuals for all observations. Compute a correlation between length of stay and the predicted values (this correlation is called the coefficient of multiple correlation – refer to MLR 1.pdf lecture note). Manually calculate the square of the correlation coefficient and verify this is equal to R2 that you obtained in part c) above.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mfBEoOjXDCgT",
        "colab_type": "code",
        "outputId": "922c26aa-cc2f-4286-ee10-12d6a20ec74b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "data['predicted'] = model1.predict()\n",
        "data[['predicted', 'los']].corr().values[1][0]**2"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.34904056453790605"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jkEh9Dhmv-06",
        "colab_type": "text"
      },
      "source": [
        "The R-squared is the same as the value in part c)\n",
        "\n",
        "---\n",
        "\n",
        "e. Using the data set you just created above, run four different tests for normality of residuals in Model 1. Also show a normal probability plot of residuals. Are residuals normally distributed? Comment on your finding."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VnECyyzCwJk9",
        "colab_type": "code",
        "outputId": "28a5bc7e-1db0-4b86-bd22-5e3b37912aa2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        }
      },
      "source": [
        "# het_white, het_arch, het_breuschpagan, HetGoldfeldQuandt\n",
        "\n",
        "data['residual'] = model1.resid\n",
        "\n",
        "trash_tuple = stats.probplot(x=model1.resid, plot=sns.mpl.pyplot, fit=True)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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cKCws5KOPPsLd3b2m3W+bv78/KSkplJWVoVKpKCsrQ6vV4u/vb/IxZG4l69dY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\nFRIOQgghqvh/CyD50SwT7n0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KwwiQQoLDRl1",
        "colab_type": "code",
        "outputId": "b0ca41aa-6b88-4461-bf26-d77c48f7f39b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 581
        }
      },
      "source": [
        "import statsmodels.stats.api as sms\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "def homoscedasticity_test(model):\n",
        "\n",
        "    fitted_vals = model.predict()\n",
        "    resids = model.resid\n",
        "    resids_standardized = model.get_influence().resid_studentized_internal\n",
        "\n",
        "\n",
        "    sns.distplot(fitted_vals)\n",
        "\n",
        "    shapiro_test = pd.DataFrame(stats.shapiro(resids),\n",
        "                              columns=['value'],\n",
        "                              index = ['W', 'p-value'])\n",
        "\n",
        "    k2_test = pd.DataFrame(stats.normaltest(resids), \n",
        "                           columns=['value'],\n",
        "                           index=['stat', 'p-value'])\n",
        "\n",
        "    and_test = pd.DataFrame(stats.anderson(resids),\n",
        "                           columns=['value'],\n",
        "                           index=['p-value', 'results1', 'results2'])\n",
        "\n",
        "    print('\\n Shapiro test ----')\n",
        "    print(shapiro_test)\n",
        "    print('\\n DAostinos K2  test ----')\n",
        "    print(k2_test)\n",
        "    print('\\n  Anderson test ----')\n",
        "    print(and_test)\n",
        "    print('\\n Histogram plot ----')\n",
        "\n",
        "homoscedasticity_test(model1)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            " Shapiro test ----\n",
            "            value\n",
            "W        0.991600\n",
            "p-value  0.732828\n",
            "\n",
            " DAostinos K2  test ----\n",
            "            value\n",
            "stat     0.148010\n",
            "p-value  0.928667\n",
            "\n",
            "  Anderson test ----\n",
            "                                        value\n",
            "p-value                              0.250425\n",
            "results1  [0.557, 0.634, 0.761, 0.888, 1.056]\n",
            "results2          [15.0, 10.0, 5.0, 2.5, 1.0]\n",
            "\n",
            " Histogram plot ----\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jibsXFqodR0SoElsqdU1ddPTI8E00k6KPUx8et9PsvDyd0qCXp4EYWaktDQX4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\nSUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cu-SGfDZ2_9t",
        "colab_type": "text"
      },
      "source": [
        "The probability plot in conjunction with the histogram, the Shapiro-Wilks test, the D'Agostino's K2 test, and the Anderson test show that the residuals are normal. \n",
        "\n",
        "---\n",
        "\n",
        "For Model 1, produce a residual plot against predicted values and against each of the three predictor variables. Also using the same model, conduct the White’s test for homoscedasticity Interpret results and state your findings."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rHlJJ8kCt7yx",
        "colab_type": "code",
        "outputId": "ea25a1d5-b0fa-4227-b127-1083e9b2a130",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "source": [
        "sns.regplot(x=data['predicted'], y=data['residual'], lowess=True, line_kws={'color': 'red'})"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7effb7ce15f8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Mx+ByNv9Rr16wYAEsWIAyYwaWuDgu3Qlq0wcFGAwGXG4Pbo+KongXjVXXOhnS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\nH05jUONrtZnAAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KkCAPRtrcl4j",
        "colab_type": "code",
        "outputId": "b61a9a08-2b5e-41f4-b456-c4054ce5637d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "source": [
        "sns.regplot(x=data['age'], y=data['residual'], lowess=True, line_kws={'color': 'red'})"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7effb7bcd710>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Zm5q8kycdDu9z+ZITaWlAdnb4fzYbkJ0NpqQEeqsVegB1yytgb3XApOtqX7of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\nkBAUHAghhIT4/0OVG43emg5ZAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iEaiQW3ncrnP",
        "colab_type": "code",
        "outputId": "4a16c814-578c-44e5-c97e-88ea12e4c202",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "source": [
        "sns.regplot(x=data['infect'], y=data['residual'], lowess=True, line_kws={'color': 'red'})"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7effb7b33668>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Pjyb0XRuUZfAV3+Cq7/dicmUZMk986/3zsWPRseR6bBg1A38/ZQLDsO7RUZIM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\nEEJ8UHIghBDig5IDIYQQH5QcCCGE+Pj/ifzXfixZ6HAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e5zPyvV2c9LY",
        "colab_type": "code",
        "outputId": "12e703e0-35cd-4bbd-99c2-aad5a18294d5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "source": [
        "sns.regplot(x=data['service'], y=data['residual'], lowess=True, line_kws={'color': 'red'})"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7effb7b1c2b0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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f3G5v5++JaojVx7Fp1VZktjcgsa0JLpsDHbGJaI9NRLMtHguumgIltbeTNw1f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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iMkXu1GL0meG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "white_test = pd.DataFrame(sms.het_white(model1.resid, model1.model.exog),\n",
        "                              columns=['value'],\n",
        "                              index = ['LM Statistic', 'LM-Test p-value', 'F-Statistic', 'F-Test p-value'])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fTuFvvi0dnQ2",
        "colab_type": "code",
        "outputId": "ca95e129-1575-41d6-f26e-ce37536258e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 174
        }
      },
      "source": [
        "white_test"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>LM Statistic</th>\n",
              "      <td>9.665167</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>LM-Test p-value</th>\n",
              "      <td>0.378265</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>F-Statistic</th>\n",
              "      <td>1.070359</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>F-Test p-value</th>\n",
              "      <td>0.391177</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                    value\n",
              "LM Statistic     9.665167\n",
              "LM-Test p-value  0.378265\n",
              "F-Statistic      1.070359\n",
              "F-Test p-value   0.391177"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lto1Cy85lqgO",
        "colab_type": "code",
        "outputId": "5be1e804-5cb5-47a1-f066-70b0744bf7e7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "print('The white test is not significant, so it is homoscedastsic. However the residual vs predicted plot shows that the data might not be linear')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The white test is not significant, so it is homoscedastsic. However the residual vs predicted plot shows that the data might not be linear\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ek7zOhYomlgF",
        "colab_type": "code",
        "outputId": "acdecd94-e5f2-4837-f705-73b0df478b6f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        }
      },
      "source": [
        "data[['los', 'age', 'infect', 'service']].describe()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>los</th>\n",
              "      <th>age</th>\n",
              "      <th>infect</th>\n",
              "      <th>service</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>111.000000</td>\n",
              "      <td>111.000000</td>\n",
              "      <td>111.000000</td>\n",
              "      <td>111.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>9.484324</td>\n",
              "      <td>53.145045</td>\n",
              "      <td>4.321622</td>\n",
              "      <td>42.907207</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>1.474732</td>\n",
              "      <td>4.447016</td>\n",
              "      <td>1.328937</td>\n",
              "      <td>15.200106</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>6.700000</td>\n",
              "      <td>38.800000</td>\n",
              "      <td>1.300000</td>\n",
              "      <td>5.700000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>8.320000</td>\n",
              "      <td>50.800000</td>\n",
              "      <td>3.600000</td>\n",
              "      <td>31.400000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>9.410000</td>\n",
              "      <td>53.000000</td>\n",
              "      <td>4.400000</td>\n",
              "      <td>42.900000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>10.405000</td>\n",
              "      <td>56.050000</td>\n",
              "      <td>5.150000</td>\n",
              "      <td>54.300000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>13.950000</td>\n",
              "      <td>65.900000</td>\n",
              "      <td>7.800000</td>\n",
              "      <td>80.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "              los         age      infect     service\n",
              "count  111.000000  111.000000  111.000000  111.000000\n",
              "mean     9.484324   53.145045    4.321622   42.907207\n",
              "std      1.474732    4.447016    1.328937   15.200106\n",
              "min      6.700000   38.800000    1.300000    5.700000\n",
              "25%      8.320000   50.800000    3.600000   31.400000\n",
              "50%      9.410000   53.000000    4.400000   42.900000\n",
              "75%     10.405000   56.050000    5.150000   54.300000\n",
              "max     13.950000   65.900000    7.800000   80.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pFV2nkU-mwrk",
        "colab_type": "code",
        "outputId": "6964738e-5184-419f-e776-c21c872d2bc1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 174
        }
      },
      "source": [
        "data[['los', 'age', 'infect', 'service']].corr()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>los</th>\n",
              "      <th>age</th>\n",
              "      <th>infect</th>\n",
              "      <th>service</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>los</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.122205</td>\n",
              "      <td>0.549467</td>\n",
              "      <td>0.367860</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>age</th>\n",
              "      <td>0.122205</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.028424</td>\n",
              "      <td>-0.056921</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>infect</th>\n",
              "      <td>0.549467</td>\n",
              "      <td>-0.028424</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.401806</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>service</th>\n",
              "      <td>0.367860</td>\n",
              "      <td>-0.056921</td>\n",
              "      <td>0.401806</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "              los       age    infect   service\n",
              "los      1.000000  0.122205  0.549467  0.367860\n",
              "age      0.122205  1.000000 -0.028424 -0.056921\n",
              "infect   0.549467 -0.028424  1.000000  0.401806\n",
              "service  0.367860 -0.056921  0.401806  1.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9VUfQM4FnDLn",
        "colab_type": "code",
        "outputId": "30e3cd4c-cc9e-4a4c-a99f-7bb217cf043d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 494
        }
      },
      "source": [
        "model1.summary(alpha=0.05)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>           <td>los</td>       <th>  R-squared:         </th> <td>   0.349</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.331</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   19.12</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Tue, 21 Jan 2020</td> <th>  Prob (F-statistic):</th> <td>5.29e-10</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>01:14:40</td>     <th>  Log-Likelihood:    </th> <td> -176.29</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>   111</td>      <th>  AIC:               </th> <td>   360.6</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>   107</td>      <th>  BIC:               </th> <td>   371.4</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "     <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>   <td>    3.8412</td> <td>    1.463</td> <td>    2.625</td> <td> 0.010</td> <td>    0.941</td> <td>    6.742</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>age</th>     <td>    0.0485</td> <td>    0.026</td> <td>    1.872</td> <td> 0.064</td> <td>   -0.003</td> <td>    0.100</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>infect</th>  <td>    0.5326</td> <td>    0.095</td> <td>    5.635</td> <td> 0.000</td> <td>    0.345</td> <td>    0.720</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>service</th> <td>    0.0178</td> <td>    0.008</td> <td>    2.150</td> <td> 0.034</td> <td>    0.001</td> <td>    0.034</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td> 0.148</td> <th>  Durbin-Watson:     </th> <td>   2.143</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.929</td> <th>  Jarque-Bera (JB):  </th> <td>   0.263</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td> 0.079</td> <th>  Prob(JB):          </th> <td>   0.877</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 2.821</td> <th>  Cond. No.          </th> <td>    884.</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:                    los   R-squared:                       0.349\n",
              "Model:                            OLS   Adj. R-squared:                  0.331\n",
              "Method:                 Least Squares   F-statistic:                     19.12\n",
              "Date:                Tue, 21 Jan 2020   Prob (F-statistic):           5.29e-10\n",
              "Time:                        01:14:40   Log-Likelihood:                -176.29\n",
              "No. Observations:                 111   AIC:                             360.6\n",
              "Df Residuals:                     107   BIC:                             371.4\n",
              "Df Model:                           3                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const          3.8412      1.463      2.625      0.010       0.941       6.742\n",
              "age            0.0485      0.026      1.872      0.064      -0.003       0.100\n",
              "infect         0.5326      0.095      5.635      0.000       0.345       0.720\n",
              "service        0.0178      0.008      2.150      0.034       0.001       0.034\n",
              "==============================================================================\n",
              "Omnibus:                        0.148   Durbin-Watson:                   2.143\n",
              "Prob(Omnibus):                  0.929   Jarque-Bera (JB):                0.263\n",
              "Skew:                           0.079   Prob(JB):                        0.877\n",
              "Kurtosis:                       2.821   Cond. No.                         884.\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_fYDQQ7lnNHb",
        "colab_type": "text"
      },
      "source": [
        "|Variable| Mean  | SD  | Correlation with LOS  |   | Estimated beta coeff  | 95% CI  |\n",
        "|---|---|---|---|---|---|---|\n",
        "|LOS| 9.484   | 1.474  | 1.00  | Intercept  | 3.8412  |  (0.941, 6.742) |\n",
        "|Age| 53.145  | 4.447  | 0.122  |   | 0.0485  | (-0.003, 0.100)  |\n",
        "|Infection Risk| 4.321  | 1.329  | 0.549   |   | 0.5326  | (0.345, 0.720)  |\n",
        "|Facilities & Services   | 42.907  | 15.2   | 0.367   |   | 0.0178  | (0.001, 0.034)  |\n",
        "|---|---|---|---|---|---|---|\n",
        "|---|---|---|---|$R^2$|0.349|---|\n",
        "|---|---|---|---|$Adjusted R^2$|0.331|---|\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V4d7uraLph7n",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}